The IEEE 802.11 wireless LAN standardisation process recently created the “high throughput” task group, which aims to generate a new standard (i.e., 802.11n) for wireless LAN systems with a measured throughput of greater than 100 Mbit/s. The dominant technology that promises to be able to deliver these increased speeds are so-called MIMO (multiple-input, multiple-output) systems. MIMO systems are defined by having multiple antennas used for both transmission and reception. The maximum theoretical throughput of such a system scales linearly with the number of antennas, which is the reason that the technology is of great interest for high throughput applications. An example of such a system is shown in FIG. 1, with a portable computer 2 transmitting to an access point where each device has three antennas TX1-TX3.
These systems can offer improved throughput compared to single antenna systems because there is spatial diversity: each piece of information transmitted from each transmitting antenna travels a different path to each receiving antenna RX1-RX3, and as noted above, experiences distortion with different characteristics (different channel transfer functions). In the example of FIG. 1, there are three different channel transfer functions from each antenna to each receiver 3: the transfer function from transmitting antenna x to receiving antenna y is denoted by Hxy. Greater capacity is obtained by making use of the spatial diversity of these independent or semi-independent channels (perhaps in conjunction with other coding techniques) to improve the chance of successfully decoding the transmitted data. The examples given here use three transmitting antennas. However, any arbitrary number of transmit antennas can be used.
The individual channel transfer functions can be collectively represented by a single channel transfer matrix H, which includes all the physical propagation effects between the transmitting antennas and the receiving antennas. Examples of such physical propagation effects include propagation delay, path loss, large-scale fading due to shadowing, small-scale fading due to multipath propagation, and scattering, diffraction and refraction effects. The channel transfer matrix H also includes various hardware characteristics effecting the signal during transmission, such as pulse shape filters, correlations due to antenna coupling or calibration errors, phase shifts due to non-ideal mixing or lack of transmitter-receiver clock synchronization, and delays due to filtering times.
In order to reconstruct the transmitted signal at the receiver various distortions have to be mitigated or removed through a process referred to as channel equalization or simply equalization. Equalization generally refers to any signal processing that is performed at the transmitter and/or the receiver that is at least partially directed to the mitigation or removal of signal distortions experienced during the transmission of signals, is at least partially directed to the mitigation or removal of interference between signals transmitted over a channel, and/or is at least partially directed to an improvement in the signal-to-noise ratio of the transmitted signal.
Currently, two types of linear equalization are often used to improve the receiver performance, namely non-adaptive linear equalization and adaptive linear equalization. Non-adaptive linear equalizers usually assume “piece-wise” stationarity of the channel and design the equalizer according to some optimization criteria such as MMSE (Minimum Mean Squared Error) or zero-forcing, which in general involves matrix inversion of the channel transfer matrix H or functions thereof such as an equalization matrix. This can be computationally expensive, especially when the coherence time of the channel is short and the equalizers have to be updated frequently. For example, the MMSE or zero-forcing equalization process in a MIMO OFDM system is performed over each sub-carrier by inverting a square matrix. The computational complexity of the problem can be appreciated by recognizing that the size of the matrix to be inverted is equal to the number of transmit antennas and the number of sub-carriers, which can vary from 64 for IEEE 802.11n systems (i.e., Wi-Fi systems) to 2048 for IEEE 802.16e systems (i.e., Wi-Max systems). On the other hand, instead of using non-adaptive linear equalizers, adaptive algorithms solve the similar LMMSE or zero-forcing optimization problems by means of stochastic gradient algorithms and avoid direct matrix inversion. Although computationally more manageable, the adaptive algorithms are less robust since their convergence behavior and performance depend on the choices of parameters such as step size.
Accordingly, it would be desirable to provide a method and apparatus for reducing the complexity of the non-adaptive linear equalization process.